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Simplifying 5x2 + -3x + 10 = 45 Reorder the terms: 10 + -3x + 5x2 = 45 Solving 10 + -3x + 5x2 = 45 Solving for variable 'x'. Reorder the terms: 10 + -45 + -3x + 5x2 = 45 + -45 Combine like terms: 10 + -45 = -35 -35 + -3x + 5x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -35 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + -0.6x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.6x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.6x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.6x + x2 = 0 + 7 -0.6x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.6x + x2 = 7 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 7 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 7 + 0.09 Combine like terms: 7 + 0.09 = 7.09 0.09 + -0.6x + x2 = 7.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 7.09 Calculate the square root of the right side: 2.662705391 Break this problem into two subproblems by setting (x + -0.3) equal to 2.662705391 and -2.662705391.Subproblem 1
x + -0.3 = 2.662705391 Simplifying x + -0.3 = 2.662705391 Reorder the terms: -0.3 + x = 2.662705391 Solving -0.3 + x = 2.662705391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 2.662705391 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.662705391 + 0.3 x = 2.662705391 + 0.3 Combine like terms: 2.662705391 + 0.3 = 2.962705391 x = 2.962705391 Simplifying x = 2.962705391Subproblem 2
x + -0.3 = -2.662705391 Simplifying x + -0.3 = -2.662705391 Reorder the terms: -0.3 + x = -2.662705391 Solving -0.3 + x = -2.662705391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -2.662705391 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.662705391 + 0.3 x = -2.662705391 + 0.3 Combine like terms: -2.662705391 + 0.3 = -2.362705391 x = -2.362705391 Simplifying x = -2.362705391Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.962705391, -2.362705391}
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